In this work, we derive a general equation describing the transmission of a probe beam in a pump/probe experiment upon optical injection of carriers into a semiconductor. The pump/probe radial overlap equation generalizes previous pump/probe approaches by considering the pump and probe beam sizes relative to each other and to the diffusion length. The pump/probe equation leverages a powerful solution to the free-carrier density under optical injection that is also derived in this work. The free-carrier density solution extends the work of Luke and Cheng to 3-dimensions, incorporating the effects of radial diffusion in a plane parallel to the semiconductor surface. The pump/probe equation quantifies the magnitude of free-carrier absorption of a probe beam induced by free-carriers optically injected via a pump beam. We show that when the pump/probe beams are much smaller than the carrier diffusion length, radial diffusion effects dominate. Measurements in this regime can be used to uniquely and simultaneously determine both the effective carrier lifetime and the diffusion coefficient. The equation agrees well with experimental measurements using a recently developed single-beam pump/probe technique, which ensures a perfect overlap of the pump and probe beams. Based on this equation, measurement criteria are developed for accurate determination of carrier lifetime and to correct for the effects of radial diffusion.
This paper presents a new type of control scheme and device for controlling gas flow into semiconductor process chambers. The key component of the Gas Flow Controller (GFC) is a high-precision valve with an integrated position sensor, which is used to maintain a constant flow rate. A map lookup scheme is employed to adjust the valve position to accommodate the upstream pressure, including any changes or disturbances. The layout of the flow controller also allows for the incorporation of a pressure-volume-time-temperature-based flow measurement, which is a primary standard flow measurement, to confirm and maintain flow accuracy throughout the device's lifetime. The fast response time of the sensors and the high sampling rate in the control loop enables the control of the gas flow within the order of tens of milliseconds.
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